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A Non-Local Reality: Is there a Phase Uncertainty in Quantum Mechanics?

A century after the advent of Quantum Mechanics and General Relativity, both theories enjoy incredible empirical success, constituting the cornerstones of modern physics. Yet, paradoxically, they suffer from deep-rooted, so-far intractable, conflicts. Motivations for violations of the notion ofrelativistic locality include the Bell's inequalities for hidden variable theories, the cosmological horizon problem, and Lorentz-violating approaches to quantum geometrodynamics, such as Horava-Lifshitz gravity. Here, we explore a recent proposal for a ``real ensemble'' non-local description of quantum mechanics, in which ``particles'' can copy each others' observables AND phases, independent of their spatial separation. We first specify the exact theory, ensuring that it is consistent and has (ordinary) quantum mechanics as a fixed point, where all particles with the same observables have the same phases. We then study the stability of this fixed point numerically, and analytically, for simple models. We provide evidence that most systems (in our study) are locally stable to small deviations from quantum mechanics, and furthermore, the phase variance per observable, as well as systematic deviations from quantum mechanics, decay as ~ (EnergyXTime)^{-n}, where n > 2. Interestingly, this convergence is controlled by the absolute value of energy (and not energy difference). Finally, we discuss different issues related to this theory, as well as potential implications for early universe, and the cosmological constant problem.